Chapter 1, Problem 1.11CP

Mott [Ref. 49, p. 38] discusses a simple falling-ball viscometer, which we can analyze later in Chap. 7. A small hall of diameter D and density $\rho$_b falls through a tube of test Liquid ( $\rho$ , $\mu$). The fall velocity V is calculated by the time to fall a measured distance. The formula for calculating the viscosity of the fluid is $\mu =\frac{({\rho }_b-\rho )g{D}^2}{18V}$

This result is limited by the requirement that the Reynolds number ( $\rho$VD/ $\mu$) be less than 1.0. Suppose a steel hall (SG — 7. 87) of diameter 2.2 mm falls in SAE 25W oil (SG = 0.88) at 20°C. The measured fall velocity is 8,4 cm/s. (a) What is the viscosity of the oil, in kg/m-s? (b) Is the Reynolds number small enough for a valid estimate?